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Lubov Fominskaja [6]

3 years ago

15

How do you solve 6) n2+7n+15=5 by factoring?

1 answer:

charle [14.2K]3 years ago

8 0

First, you need to set the equation equal to zero:

n^2 + 7n + 10 = 0

Now we factor. We need to find two numbers that add up to 7 and multiply to 10.

2 + 5 = 7
2 * 5 = 10

Now, we just need to write this as a polynomial:

(n + 2) (n + 5)
is our answer.

Hope this helps!

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The width of a rectangle is 4 inches greater than half the length. The perimeter is 56 inches. What is the length and the width

yulyashka [42]

Answer:

Length of the rectangle = 16 inches

Width of the rectangle = 12 inches

Step-by-step explanation:

Let the length of the rectangle be represented by x.

Then width can be expressed as $\[\frac{x}{2}+4\]
$

Perimeter of a rectangle is the sum of four sides of the rectangle.

This can be expressed as 2*(length + breadth)

= $2* (x + \frac{x}{2}+4)$

= $2* (\frac{3x}{2}+4)$

= $3x + 8$

But perimeter is given as 56.

So, $\[3x + 8 = 56\]
$

=> $3x = 48$

=> $x = 16$

Hence length of the rectangle = 16 inches

Width of the rectangle = $\frac{16}{2}+4$ = 12 inches

7 0

3 years ago

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Give a decimal number that is less than 23.7 and greater than 23.7

Makovka662 [10]

I think you are asking for two numbers, so you just have to look at the decimals.

23.7

We can use an infinite amount of numbers here, but to make it simple you can just take away 0.01 or add 0.01.

23.69
23.71

These are funny answers as well because they both round to 23.7 and meet the requirements.

3 0

3 years ago

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Fine length of BC on the following photo.

MrMuchimi

Answer:

$BC=4\sqrt{5}\ units$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ACD

Find the length side AC

Applying the Pythagorean Theorem

$AC^2=AD^2+DC^2$

substitute the given values

$AC^2=16^2+8^2$

$AC^2=320$

$AC=\sqrt{320}\ units$

simplify

$AC=8\sqrt{5}\ units$

step 2

In the right triangle ACD

Find the cosine of angle CAD

$cos(\angle CAD)=\frac{AD}{AC}$

substitute the given values

$cos(\angle CAD)=\frac{16}{8\sqrt{5}}$

$cos(\angle CAD)=\frac{2}{\sqrt{5}}$ ----> equation A

step 3

In the right triangle ABC

Find the cosine of angle BAC

$cos(\angle BAC)=\frac{AC}{AB}$

substitute the given values

$cos(\angle BAC)=\frac{8\sqrt{5}}{16+x}$ ----> equation B

step 4

Find the value of x

In this problem

$\angle CAD=\angle BAC$ ----> is the same angle

so

equate equation A and equation B

$\frac{8\sqrt{5}}{16+x}=\frac{2}{\sqrt{5}}$

solve for x

Multiply in cross

$(8\sqrt{5})(\sqrt{5})=(16+x)(2)\\\\40=32+2x\\\\2x=40-32\\\\2x=8\\\\x=4\ units$

$DB=4\ units$

step 5

Find the length of BC

In the right triangle BCD

Applying the Pythagorean Theorem

$BC^2=DC^2+DB^2$

substitute the given values

$BC^2=8^2+4^2$

$BC^2=80$

$BC=\sqrt{80}\ units$

simplify

$BC=4\sqrt{5}\ units$

7 0

3 years ago

Troy puts $200.00 into an account to use for school expenses. The account earns 7% interest, compounded annually. How much will

storchak [24]

Answer:

the final amount is = $280.51

Step-by-step explanation:

The standard formula for compound interest is given as;

A = P(1+r/n)^(nt) .....1

Given that;

Principal P = $200

Interest rate r = 7% = 0.07

Time t = 5 years

Final amount = A

Number of time compounded per year n = 1

Substituting the values;

A = 200(1+0.07/1)^(1×5)

A = 280.51

Therefore, the final amount is = $280.51

7 0

4 years ago

Which is greater between |5| amd |2|

pshichka [43]

Answer:

|5| = 5 and |2| = 2 and because 5 > 2, our answer is |5| > |2|.

8 0

3 years ago

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